Let \(k\)  be an algebraically closed field of characteristic 0.
Let the base scheme \(S\)  be connected, noetherian and of finite type over \(k\) .
Each Deligne-Mumford \(S\) -stack is assumed to be separated, notherian and of finite type over \(S\) . One may refer to [[1]}, [2]}, [3]}, [4]}] for the notion of stacks and their properties.
It is shown in [[5]}, [6]}] that a Deligne-Mumford stack \(\mathcal {X}\)  over \(S\)  has a coarse moduli space \(\pi :\mathcal {X}\rightarrow X\)  which is proper and quasi-finite. When \(X\)  is a scheme, we simply call it a moduli scheme. Denote by \(\mathrm {QCoh}\)  the category of quasi-coherent sheaves.
